A point in three-dimensional space can be represented in a three-dimensional coordinate system . In such a case, a z -axis is taken perpendicular to both the x - and y -axes . A point P is assigned an ordered triple P x , y , z relative to a fixed origin where the three axes meet. For Exercises 83-86, determine the distance between the two given points in space. Use the distance formula d = x 2 − x 1 2 + y 2 − y 1 2 + z 2 − z 1 2 . 9 , − 5 , − 3 and 2 , 0 , 1
A point in three-dimensional space can be represented in a three-dimensional coordinate system . In such a case, a z -axis is taken perpendicular to both the x - and y -axes . A point P is assigned an ordered triple P x , y , z relative to a fixed origin where the three axes meet. For Exercises 83-86, determine the distance between the two given points in space. Use the distance formula d = x 2 − x 1 2 + y 2 − y 1 2 + z 2 − z 1 2 . 9 , − 5 , − 3 and 2 , 0 , 1
Solution Summary: The author calculates the distance between the two points (9,-5,-3) and
A point in three-dimensional space can be represented in a three-dimensional coordinate system. In such a case, a
z
-axis
is taken perpendicular to both the
x
- and
y
-axes
.
A point
P
is assigned an ordered triple
P
x
,
y
,
z
relative to a fixed origin where the three axes meet. For Exercises 83-86, determine the distance between the two given points in space. Use the distance formula
d
=
x
2
−
x
1
2
+
y
2
−
y
1
2
+
z
2
−
z
1
2
.
9
,
−
5
,
−
3
and
2
,
0
,
1
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
T
1
7. Fill in the blanks to write the calculus problem that would result in the following integral (do
not evaluate the interval). Draw a graph representing the problem.
So
π/2
2 2πxcosx dx
Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
38,189
5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the
solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
≤
and the curve y
y =
about the line
x =
=플
2
80
F3
a
FEB
9
2
7
0
MacBook Air
3
2
stv
DG
Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x.
h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1
-
-
-
f(x) = ☐
University Calculus: Early Transcendentals (4th Edition)
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